We ALL know the proper name for it, and we ALL know the "slang" or "TV" or "American" name for it, and no one, certainly on my BMQ course really cares what the course is referred to informally.
I wouldn‘t tell the OC that I had a great time at his "boot camp" but most of the rest of the staff, etc., will know what you are talking about and won‘t raise a fuss.
I understand it is important to maintain our identity as being separate from the US, and that one should endeavour to use the proper names for things, but really... who cares? Boot camp, basic, BMQ, GMT, it all refers to pretty much the same damn thing. I suggest using the small white pill marked "Tylenol". Take several and relax.